Eh.... ignore that. The part about balloon flight and contact irrelevant, not the focus.
I just think of the societal implications.
Well, gosh, Accelerator, until someone tries to make contact there will be very little for people to go on. The net impact would be limited. You don't say when it first appears. I am going to assume, before ordinary humans on the ground develop agriculture--so, no later than the end of the last glacial period. How long it might have been aloft prior to that is open ended. The local gatherer-hunter peoples who live in line of sight of it will have some story to tell about it, but they might as well be stories about the Moon. To be sure there is that lake underneath, which one might guess is where the city was built before it went aloft, the divot left in the bedrock by its removal and ascent, but gatherer-hunter peoples have not got experience making cities so they might or might not theorize the base of the city seen from below would fit into the basin. Nor did you specify it would--I imagine based on what you say, it does, but you could make it bigger or smaller just to gainsay this theory I guess.
So, people living off the land would exist in small number, just a half thousand or so in direct eyeshot of it at any time in their lives I guess--depending on how it is above the local terrain. To these bands it has always been there and its phenomena are in the same category as speculations about clouds or the heavens. Since people can hear sounds like music I suppose they will have firmer ground than usual to populate it with spirits or more or less divine people, but humans do that anyway. (I suspect we have a built in set of neural mechanisms that tend to cause us to project human type intent on all kinds of things, which is functional in our evolved environment--even mindless things follow patterns and supposed this is out of intent is a way of narratively tracking useful observations of their "character." I suspect this development, narrating the existence of surmised intentional beings with agendas and desires, was perhaps the key evolutionary event defining the modern species. It is actually, objectively speaking, irrational, but it serves us well). So matters stand for thousands of years. Eventually, as agriculture spreads and the tendency to develop permanently settled villages and megalithic projects (often intelligible as basically astronomical, assisting with star and planet sightings as well as tracking sun and moon) the people living within eye-shot and easy travel to that vicinity tend to be inspired to adopt towns and make larger cities a bit precociously, with the encouragement of the sky model to inspire them. And the mythic function will probably become a dwelling place for their favored pantheons, unless the memory of ancient lore (which is surprisingly persistent and oddly accurate some of the times we can get independent verification) insists that the place was there long before the ancestors of the current lot invaded, and therefore the gods up there cannot be the ones the current lot's ancestors brought in with them. Don't know if that basic logic will be allowed to prevail or if revisionism will creep in to reconcile historic memory with the egotism of a particular dominant order...for instance the myth might grow from random roots, among people who vaguely know their ancestors invaded some thousand years ago or so, that the migration was caused by their gods, who had in fact always dwelt in this visible heaven, and sought to bring their followers into the view of it from afar. In one century this might be a bit of far-fetched "Fanfic" as it were, connecting dots of legend that had much more reasonable separate explanations, then as the idea inspires it elaborates, the pragmatic roots of the traditional story "evidence" are downplayed and largely forgotten while the elaborations become more and more pointed and skeptics shake their heads in silence; a couple centuries later it is universally taught dogma and no one remembers the skeptics; it is now established fact that the gods always were their own pantheon and there is no contradiction seen with legendary memories of migrating in from thousands of miles away.
And so matters rest until one of two things happen: either the region is the cradle of a major advanced religion, one that can become dominant for post-imperial, medieval and early modern gunpowder civilzations, and the mythology of this unattainable sky paradise is woven right into it. Or instead such a religion invades from outside. Say this sky city is hovering above southwestern Britain--I wonder if the Celtic peoples known to the Romans in Caesar's time would have been there long enough to claim the sky city for their pantheon or just acknowledge it is some sort of fairy kingdom and leave it at that. Sky Sidhe. The Romans come in under Claudius--they've heard of this sky city, it one of the exotic wonders of the world. But it doesn't do anything to impede their gradual conquest.
Well not much...suppose that the city is low enough that some kind of mirrors, sheets of polished bronze or even coated with silver somehow, can shine reflections on the base that people can see very far away. It is now possible for people based near the city to bounce visual heliographic signals, so that people who are more distant can read them; over the range this is possible, a commander based near the city has a communications advantage of sorts. To be sure their enemies can see the signals as readily as their own troop commanders, but the locals know the code, the invaders do not. This might be an effective force multiplier. But resistant British tribes would need a lot more force multiplication that that to stave off their doom! During the Roman period, the sky heliograph effect was noted and recorded, and written up in various Roman books, and Roman forces stationed in southwest Britain took advantage themselves, setting up a regional HQ there and using the sky city to flash general edicts to relays close enough to see, thus speeding up communications a bit. When the Roman legions were withdrawn, the local lords had some idea how to use this system and consolidated a defensive unit--from these days to modern times, a circular region centered on the sky city develops and maintains a distinct political identity named after the city, in various languages--for this realm is still not immune to conquest, just more resistant than a simple weighing of its resources would indicate. For a time the Britons hold out against the Saxons extra long on this front line, and the conquest of Cornwall into England is delayed, and the circular zone becomes an English distinct lordship as it had been distinct under the Cymru. In turn when William's invaders conquer England the English rally and hold on that front a year or so, before collapsing, and the zone becomes a county in the Norman hierarchy, with special specified duties to speed the King's messages along and serve as a bastion of his rule. It remains distinct and sometimes important whenever civil war or invasion wracks England.
But there the matter rests. Other than aiming large mirrors at it to flash signals to people in the surrounds, there is no practical use. No one can climb up. I presume from your descripition no one ever comes down to be questioned or captured. It might as well be a natural phenomenon, some kind of permanant cloud bank or optical illlusion. Realms and religions come and go and wise priests and other theocrats learn, if it was not obvious up front, that ranting against it as pagan or devilish or any such thing does them no good, because there is nothing they can do to banish from the skies and it only makes them look weak trying. Sitting above the region of Glastonbury, the cultural consensus is that it is Avalon of the Arthurian legend, and the legendary court of Arthur had its support and blessing, implying a vague alignment with Christian providence. Perhaps various radical Protestants despise these superstitions and suspect it must be Satanic somehow or other and discourage any attention to it, but they are in the minority since it sits there and exists. The various kingdoms controlling the ground below use it for signal relays, and otherwise it is left to legend and speculation, as real as the Moon in the sky and just as unattainable and less relevant.
And this brings us to modern times, starting around the English Civil War and after...and wherever in the world it might be situated, that is the over all arc of its significance. Whenever a modern scientific mentality and school develops and the place where it floats is brought into that movement's ken, it will come under scrutiny just as the planets do. Maybe it would disrupt acceptance of Newtonian physics---after all, for the action of the fact that what looks like a heavy solid mass not falling, where is the reaction on Earth? But Newtonians will probably explain it away with a handwave...still, it might deter some people from taking Newton as seriously as they did OTL.
Everything changes when balloons are developed. The latest before a major landing attempt would be 1920 I would think, using an airship.
